STEAM is your friend.
As a fan of photography, I'll use that as an example. The average person would probably consider photography to be a form of art, but took a look at the inside of any DSLR (or any camera) and just think about the engineering that went into this creative expression. It's pretty remarkable if you understand how cameras work! There are so many technologies that have used art as their motivation for creation and innovation
Think outside the box!